# 5.2.2 Work Done & Energy Transfer

### Units for Work & Energy

• The formula for work is:

W = F × s

• Multiplying force and distance produces units of newton-metres (N m)
• Work is measured in Joules (J)
• This leads to a simple conversion:

1 J = 1 N m

• Therefore, the number of Joules is equal to the number of newton-metres, making conversions between the units very straightforward, for example:

1000 J = 1000 N m

• One Joule is equal to the work done by a force of one newton acting through one metre

#### Exam Tip

You must include the correct units in your answer, forgetting to include units will lose you a mark – in the case of work, you may use either newton-metres (N m) or Joules (J)

### Work Done & Energy Transfer

• Whenever any work is done, energy gets transferred (mechanically) from one store to another
• The amount of energy transferred (in joules) is equal to the work done (also in joules)

energy transferred (J) = work done (J)

• If a force acts in the direction that an object is moving, then the object will gain energy (usually in the form of kinetic energy)
• If the force acts in the opposite direction to the movement then the object will lose energy (usually as heat)
• Common forms of energy that work can be transferred to:
• Kinetic Energy, when speeding an object up
• Gravitational Potential Energy, when raising an object higher
• Thermal Energy, in heating the object up
• Sound Energy, in producing noise
• Take the example of an object which is pushed horizontally with a 100 N force a distance of 10 m
• The work done on the object is equal to:

W = F × s

W = 100 N × 10 m = 1000 N m

• This work transferred energy to the object in the form of kinetic energy
• The object started with no kinetic energy and now has 1000 J of kinetic energy

#### Worked Example

A woman draws a bucket up out of a well. The bucket has a mass of 10 kg when filled with water and the well is 15 m deep. Take the gravitational field strength to be 9.8 N/kg. a) Describe the energy transfer involved in raising the bucket out of the well

b) Calculate the energy transferred to the bucket

Part (a)

• Work is done by the woman as she exerts a force on the rope to pull the bucket up
• The work done on the bucket is due to overcoming the weight of the bucket for a distance of 15 m
• As the bucket rises, the work done is stored as gravitational potential energy

Part (b)

Step 1: List all of the known values

• Mass, m = 10 kg
• Gravitational field strength, g = 9.8 N/kg
• Height, h = 15 m

Step 2: Write the equation relating work, force and distance

Work = Force × Distance

Step 3: Write out the equation for weight and substitute it into the work equation

Weight = m × g

Work = m × g × h

• Note: This is the equation for gravitational potential energy

Step 4: Calculate the work done on the bucket

Work = 10 × 9.8 × 15 = 1470 N m

Step 5: Convert the work done into energy transferred

Energy transferred in Joules = Work done in newton-metres

Energy transferred = 1470 J

• The bucket gained 1470 J of gravitational potential energy

#### Exam Tip

Remember:

• Changes in speed are related to kinetic energy
• Changes in height are related to gravitational potential energy
• Changes in the shape of materials are related to elastic potential energy ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
Close Close